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 RowBox[{
  RowBox[{
   RowBox[{
    RowBox[{"RefractionAngle", "::", "usage"}], "=", 
    "\"\<RefractionAngle[\!\(\*SubscriptBox[\(\[Theta]\), \
\(i\)]\),\!\(\*SubscriptBox[\(n\), \(i\)]\),\!\(\*SubscriptBox[\(n\), \
\(j\)]\)] Calculates refraction angle from normal in medium j at the boundary \
of mediem i and j using Snell's Law.\>\""}], ";"}], 
  "\[IndentingNewLine]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{
    RowBox[{"FresnelA", "::", "usage"}], "=", 
    "\"\<FresnelA[\\\"coefficient\\\",\!\(\*SubscriptBox[\(\[Theta]\), \(i\)]\
\),\!\(\*SubscriptBox[\(n\), \(i\)]\),\!\(\*SubscriptBox[\(n\), \(j\)]\)] \n\
calculates Fresnel amplitude coefficient for \!\(\*SubscriptBox[\(\[Theta]\), \
\(i\)]\) angle of incidence from normal in medium i at a planar boundary \
between medium i and medium j with refractive indices \
\!\(\*SubscriptBox[\(n\), \(i\)]\) and \!\(\*SubscriptBox[\(n\), \(j\)]\). \
Angle of Refraction \!\(\*SubscriptBox[\(\[Theta]\), \(j\)]\) is internally \
calculated using Snell's law. Eqs. 8-11.\n\n\\\"coefficient\\\" = \\\"rs\\\" \
or \\\"rp\\\" for reflection\n\\\"coefficient\\\" = \\\"ts\\\" or \\\"tp\\\" \
for transmission\n\n\
FresnelA[\\\"coefficient\\\",\!\(\*SubscriptBox[\(\[Theta]\), \
\(i\)]\),\!\(\*SubscriptBox[\(\[Theta]\), \(j\)]\),\!\(\*SubscriptBox[\(n\), \
\(i\)]\),\!\(\*SubscriptBox[\(n\), \(j\)]\)] is FresnelA with \
\!\(\*SubscriptBox[\(\[Theta]\), \(j\)]\) specified.\>\""}], ";"}], 
  "\[IndentingNewLine]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{
    RowBox[{"RefractionMv", "::", "usage"}], "=", 
    "\"\<RefractionM[\\\"pol\\\",\!\(\*SubscriptBox[\(\[Theta]\), \(v - \
1\)]\),\!\(\*SubscriptBox[\(\[Theta]\), \(v\)]\),\!\(\*SubscriptBox[\(n\), \
\(v - 1\)]\),\!\(\*SubscriptBox[\(n\), \(v\)]\)] gives the matrix of \
refraction at interface v of a thin film system for \\\"pol\\\"-polarized \
input beam. Eq. 6. \n\n\\\"pol\\\" = \\\"s\\\" or \\\"p\\\" \>\""}], ";"}], 
  "\[IndentingNewLine]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{
    RowBox[{"PhaseMv", "::", "usage"}], "=", 
    "\"\<PhaseM[\[Omega],\!\(\*SubscriptBox[\(\[Theta]\), \
\(v\)]\),\!\(\*SubscriptBox[\(n\), \(v\)]\),\!\(\*SubscriptBox[\(d\), \
\(v\)]\)] gives the phase matrix of layer v. Eq. 12\>\""}], ";"}], 
  "\[IndentingNewLine]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"AbelesS", "::", "usage"}], "=", 
   "\"\<AbelesS[\\\"pol\\\",\[Omega],{{\!\(\*SubscriptBox[\(\[Theta]\), \
\(0\)]\),\!\(\*SubscriptBox[\(n\), \
\(0\)]\)},{\!\(\*SubscriptBox[\(\[Theta]\), \
\(1\)]\),\!\(\*SubscriptBox[\(n\), \(1\)]\),\!\(\*SubscriptBox[\(d\), \
\(1\)]\)}..{\!\(\*SubscriptBox[\(\[Theta]\), \
\(k\)]\),\!\(\*SubscriptBox[\(n\), \(k\)]\),\!\(\*SubscriptBox[\(d\), \
\(k\)]\)},{\!\(\*SubscriptBox[\(\[Theta]\), \(k + \
1\)]\),\!\(\*SubscriptBox[\(n\), \(k + 1\)]\)}}] calculates the total system \
transfer matrix at frequency \[Omega] with specified material refaction \
angles \!\(\*SubscriptBox[\(\[Theta]\), \(i\)]\), refractive indices \
\!\(\*SubscriptBox[\(n\), \(i\)]\), and thin film layer thicknesses \
\!\(\*SubscriptBox[\(d\), \(i\)]\).  Eq. 15\>\""}], ";"}], "\n", 
 RowBox[{
  RowBox[{
   RowBox[{"AbelesSIv", "::", "usage"}], "=", 
   "\"\<AbelesSIv[\\\"pol\\\",\[Omega],{{\!\(\*SubscriptBox[\(\[Theta]\), \(0\
\)]\),\!\(\*SubscriptBox[\(n\), \(0\)]\)},{\!\(\*SubscriptBox[\(\[Theta]\), \
\(1\)]\),\!\(\*SubscriptBox[\(n\), \(1\)]\),\!\(\*SubscriptBox[\(d\), \
\(1\)]\)}..{\!\(\*SubscriptBox[\(\[Theta]\), \(v - 1\)]\),\!\(\*SubscriptBox[\
\(n\), \(v - 1\)]\),\!\(\*SubscriptBox[\(d\), \(v - \
1\)]\)},{\!\(\*SubscriptBox[\(\[Theta]\), \(v\)]\),\!\(\*SubscriptBox[\(n\), \
\(v\)]\)}},v] calculates the partial system transfer matrix for subsystem I \
at layer v for frequency \[Omega] with specified material refaction angles \!\
\(\*SubscriptBox[\(\[Theta]\), \(i\)]\), refractive indices \
\!\(\*SubscriptBox[\(n\), \(i\)]\), and thin film layer thicknesses \
\!\(\*SubscriptBox[\(d\), \(i\)]\).  Eq. 21\>\""}], ";"}], "\n", 
 RowBox[{
  RowBox[{
   RowBox[{
    RowBox[{"AbelesSIIv", "::", "usage"}], "=", 
    "\"\<AbelesSIIv[\\\"pol\\\",\[Omega],{{\!\(\*SubscriptBox[\(\[Theta]\), \
\(v\)]\),\!\(\*SubscriptBox[\(n\), \
\(v\)]\)},{\!\(\*SubscriptBox[\(\[Theta]\), \(v + \
1\)]\),\!\(\*SubscriptBox[\(n\), \(v + 1\)]\),\!\(\*SubscriptBox[\(d\), \(v + \
1\)]\)}..{\!\(\*SubscriptBox[\(\[Theta]\), \(k\)]\),\!\(\*SubscriptBox[\(n\), \
\(k\)]\),\!\(\*SubscriptBox[\(d\), \
\(k\)]\)},{\!\(\*SubscriptBox[\(\[Theta]\), \(k + \
1\)]\),\!\(\*SubscriptBox[\(n\), \(k + 1\)]\)}},v] calculates the partial \
system transfer matrix for subsystem II at layer v for frequency \[Omega] \
with specified material refaction angles \!\(\*SubscriptBox[\(\[Theta]\), \(i\
\)]\), refractive indices \!\(\*SubscriptBox[\(n\), \(i\)]\), and thin film \
layer thicknesses \!\(\*SubscriptBox[\(d\), \(i\)]\).  Eq. 22\>\""}], ";"}], 
  "\[IndentingNewLine]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"TransmitTopS", "::", "usage"}], "=", 
   "\"\<TransmitTopS[\[CapitalSigma]] calculates the transmission coefficient \
for incidence from the top side through transfer matrix \[CapitalSigma], \
where \[CapitalSigma] can be S, SI, or SII. Eqs. 18, 27, and 40. \>\""}], 
  ";"}], "\n", 
 RowBox[{
  RowBox[{
   RowBox[{"ReflectTopS", "::", "usage"}], "=", 
   "\"\<ReflectTopS[\[CapitalSigma]] calculates the reflection coefficient \
for incidence from the top side through transfer matrix \[CapitalSigma], \
where \[CapitalSigma] can be S, SI, or SII. Eqs. 17 and 30.\>\""}], 
  ";"}], "\n", 
 RowBox[{
  RowBox[{
   RowBox[{"TransmitBottomS", "::", "usage"}], "=", 
   "\"\<TransmitBottomS[\[CapitalSigma]] calculates the transmission \
coefficient for incidence from the bottom side through transfer matrix \
\[CapitalSigma], where \[CapitalSigma] can be S, SI, or SII.  Eqs. 20, 29, \
and 39.\>\""}], ";"}], "\n", 
 RowBox[{
  RowBox[{
   RowBox[{
    RowBox[{"ReflectBottomS", "::", "usage"}], "=", 
    "\"\<ReflectBottomS[\[CapitalSigma]] calculates the reflection \
coefficient for incidence from the bottom side through transfer matrix \
\[CapitalSigma], where \[CapitalSigma] can be S, SI, or SII. Eqs. 19 and \
28.\>\""}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", 
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    RowBox[{"InternalTransferC", "::", "usage"}], "=", 
    "\"\<InternalTransferC[\\\"method\\\",\\\"xPosDir\\\",\\\"inPosDir\\\",\!\
\(\*SubscriptBox[\(SI\), \(v\)]\),\!\(\*SubscriptBox[\(PhaseM\), \
\(v\)]\),\!\(\*SubscriptBox[\(SII\), \(v\)]\)] calculates the internal \
transfer coefficient for an externally incident wave with \\\"xPosDir\\\" \
position and directionality to an internal wave with \\\"inPosDir\\\" \
position and directionality adjacent to an interface.  Eqs. 23-26 and 31-38. \
\n\n\\\"method\\\"= \\\"SII\\\" (Eqs. 23-26) or \\\"PartialSTC\\\" (Eqs. \
31-38)\n\\\"xPosDir\\\" = \\\"0-\\\" or \\\"kp1+'\\\"\n\\\"inPosDir\\\" = \
\\\"v-'\\\" or \\\"v+'\\\" for \!\(\*SubscriptBox[\(SI\), \(v\)]\) \
\!\(\*SubscriptBox[\(Phi\), \(v\)]\) \!\(\*SubscriptBox[\(SII\), \(v\)]\) or\n\
\\\"inPosDir\\\" = \\\"v-\\\" or \\\"v+\\\" for \!\(\*SubscriptBox[\(SI\), \
\(v - 1\)]\) \!\(\*SubscriptBox[\(Phi\), \(v - 1\)]\) \
\!\(\*SubscriptBox[\(SII\), \(v - 1\)]\)\>\""}], ";"}], "\[IndentingNewLine]",
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   "\"\<ExternalTransferC[\\\"inPosDir\\\", \\\"xPosDir\\\", \
\!\(\*SubscriptBox[\(SI\), \(v\)]\), \!\(\*SubscriptBox[\(Phi\), \(v\)]\), \!\
\(\*SubscriptBox[\(SII\), \(v\)]\)] calculates the external transfer \
coefficient for a wave generated at intervace v.  Eqs. 41-44.\n\n\
\\\"xPosDir\\\" = \\\"0+\\\" or \\\"kp1-'\\\" depending on which side of the \
system the detector lays.\n\\\"inPosDir\\\" = \\\"v+\\\" for \
\!\(\*SubscriptBox[\(SI\), \(v - 1\)]\) \!\(\*SubscriptBox[\(PhaseM\), \(v - \
1\)]\) \!\(\*SubscriptBox[\(SII\), \(v - 1\)]\)\n\\\"inPosDir\\\" = \\\"v-'\\\
\" for \!\(\*SubscriptBox[\(SI\), \(v\)]\) \!\(\*SubscriptBox[\(PhaseM\), \(v\
\)]\) \!\(\*SubscriptBox[\(SII\), \(v\)]\)\>\""}], 
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